Recently, pre-trained models for music information retrieval based on self-supervised learning (SSL) are becoming popular, showing success in various downstream tasks. However, there is limited research on the specific meanings of the encoded information and their applicability. Exploring these aspects can help us better understand their capabilities and limitations, leading to more effective use in downstream tasks. In this study, we analyze the advanced music representation model MusicFM and the newly emerged SSL model MuQ. We focus on three main aspects: (i) validating the advantages of SSL models across multiple downstream tasks, (ii) exploring the specialization of layer-wise information for different tasks, and (iii) comparing performance differences when selecting specific layers. Through this analysis, we reveal insights into the structure and potential applications of SSL models in music information retrieval.